Prague Stringology Conference 2018

Two strings of equal length are said to parameterized match
if there is a bijection that maps the characters of one string to those
of the other string, so that two strings become identical.
The parameterized pattern matching problem is,
given two strings T and P, to find
the occurrences of substrings in T that parameterized match P.
Diptarama et al. [Position Heaps for Parameterized Strings, CPM 2017]
proposed an indexing data structure called parameterized position heaps,
and gave a left-to-right online construction algorithm.
In this paper, we present a right-to-left online construction
algorithm for parameterized position heaps.
For a text string T of length n over two kinds of alphabets
Σ and Π of respective size σ and π,
our construction algorithm runs in O(n log(σ + π)) time
with O(n) space.
Our right-to-left parameterized position heaps support
pattern matching queries in O(m log(σ + π) + m π + pocc)) time,
where m is the length of a query pattern P
and pocc is the number of occurrences to report.
Our construction and pattern matching algorithms are
as efficient as Diptarama et al.'s algorithms.